Question

1. $\begin{cases} x + 3y = -15 \\ y = -7 end{cases}$

solution:

1. $\begin{cases} y = x + 5 \\ x - y = 2 end{cases}$

solution:

1. $\begin{cases} 3x - 5y = -35 \\ 2x + y = -6 end{cases}$

solution:

1. $\begin{cases} x = -2 \\ 3x - 2y = -18 end{cases}$

solution:

Explanation:

Problem 5

Step1: Substitute $y=-7$ into first equation

$x + 3(-7) = -15$

Step2: Simplify to solve for $x$

$x - 21 = -15 \implies x = -15 + 21 = 6$

Problem 6

Step1: Substitute $y=x+5$ into second equation

$x - (x+5) = 2$

Step2: Simplify and solve for $x$

$x - x - 5 = 2 \implies -5=2$ (no solution, parallel lines)

Problem 7

Step1: Isolate $y$ from second equation

$y = -6 - 2x$

Step2: Substitute into first equation

$3x - 5(-6 - 2x) = -35$

Step3: Simplify to solve for $x$

$3x + 30 + 10x = -35 \implies 13x = -65 \implies x = -5$

Step4: Find $y$ using $x=-5$

$y = -6 - 2(-5) = -6 + 10 = 4$

Problem 8

Step1: Substitute $x=-2$ into second equation

$3(-2) - 2y = -18$

Step2: Simplify to solve for $y$

$-6 - 2y = -18 \implies -2y = -12 \implies y = 6$

Answer:

Problem 5: $(6, -7)$
Problem 6: No solution
Problem 7: $(-5, 4)$
Problem 8: $(-2, 6)$